Metanalysis of flow state on women caused by (stMale)

Geiser C. Challco geiser@alumni.usp.br

Initial Variables and Loading Data

env <- "stMale"
gender <- "women"
to_remove <- c('S11')
sub.groups <- c("age","ed.level","intervention","age:intervention",
                "ed.level:intervention","age:ed.level:intervention")
dat <- read_excel("../data/data-without-outliers.xlsx", sheet = "fss-env.gender-descriptive")
dat <- dat[!dat$study %in% to_remove, ]

leg <- read_excel("../data/data-without-outliers.xlsx", sheet = "legend")
## New names:
## • `` -> `...10`
leg <- leg[!leg$study %in% to_remove, ]

idx.e <- which(dat$env == env & dat$gender == gender)
idx.c <- which(dat$env == "control" & dat$gender == gender)

data <- data.frame(
  study = dat$study[idx.c],
  n.e = dat$N[idx.e], mean.e = dat$M.emms[idx.e], sd.e = dat$SD.emms[idx.e],
  n.c = dat$N[idx.c], mean.c = dat$M.emms[idx.c], sd.c = dat$SD.emms[idx.c]
)
for (cgroups in strsplit(sub.groups,":")) {
  data[[paste0(cgroups, collapse = ":")]] <- sapply(data$study, FUN = function(x) {
    paste0(sapply(cgroups, FUN = function(namecol) leg[[namecol]][which(x == leg$study)]), collapse = ":")
  })
}
data[["lbl"]] <- sapply(data$study, FUN = function(x) leg$Note[which(x == leg$study)])

Perform meta-analyses

m.cont <- metacont(
  n.e = n.e, mean.e = mean.e, sd.e = sd.e, n.c = n.c, mean.c = mean.c, sd.c = sd.c,
  studlab = lbl, data = data, sm = "SMD", method.smd = "Hedges",
  fixed = F, random = T, method.tau = "REML", hakn = T, title = paste("Flow state for",gender,"in",env)
)
summary(m.cont)
## Review:     Flow state for women in stMale
## 
##                               SMD             95%-CI %W(random)
## S1                         0.5991 [-0.0366;  1.2348]       12.9
## S2                        -0.1546 [-0.6948;  0.3856]       14.4
## S3                        -0.3863 [-1.0761;  0.3035]       12.2
## S4                         0.7135 [-0.0246;  1.4516]       11.5
## S5                         0.1435 [-0.5478;  0.8348]       12.1
## S6                         0.6749 [-0.0769;  1.4266]       11.3
## S7                        -0.3427 [-0.9389;  0.2536]       13.5
## S10: Only use prompt msgs -0.8127 [-1.5118; -0.1136]       12.0
## 
## Number of studies combined: k = 8
## Number of observations: o = 298
## 
##                         SMD            95%-CI    t p-value
## Random effects model 0.0401 [-0.4281; 0.5083] 0.20  0.8453
## 
## Quantifying heterogeneity:
##  tau^2 = 0.1887 [0.0169; 1.2175]; tau = 0.4344 [0.1300; 1.1034]
##  I^2 = 61.6% [16.9%; 82.2%]; H = 1.61 [1.10; 2.37]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  18.22    7  0.0110
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.cont, digits=2, digits.sd = 2, test.overall = T, label.e = paste0(gender,':',env))

Subgroup analysis by “age”

m.sg4sub <- update.meta(m.cont, subgroup = age, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Flow state for women in stMale
## 
##                               SMD             95%-CI %W(random)         age
## S1                         0.5991 [-0.0366;  1.2348]       12.9  adolescent
## S2                        -0.1546 [-0.6948;  0.3856]       14.4  adolescent
## S3                        -0.3863 [-1.0761;  0.3035]       12.2  adolescent
## S4                         0.7135 [-0.0246;  1.4516]       11.5       adult
## S5                         0.1435 [-0.5478;  0.8348]       12.1       adult
## S6                         0.6749 [-0.0769;  1.4266]       11.3       adult
## S7                        -0.3427 [-0.9389;  0.2536]       13.5       adult
## S10: Only use prompt msgs -0.8127 [-1.5118; -0.1136]       12.0 adolescence
## 
## Number of studies combined: k = 8
## Number of observations: o = 298
## 
##                         SMD            95%-CI    t p-value
## Random effects model 0.0401 [-0.4281; 0.5083] 0.20  0.8453
## 
## Quantifying heterogeneity:
##  tau^2 = 0.1887 [0.0169; 1.2175]; tau = 0.4344 [0.1300; 1.1034]
##  I^2 = 61.6% [16.9%; 82.2%]; H = 1.61 [1.10; 2.37]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  18.22    7  0.0110
## 
## Results for subgroups (random effects model):
##                     k     SMD             95%-CI  tau^2    tau    Q   I^2
## age = adolescent    3  0.0211 [-1.2371;  1.2793] 0.1492 0.3863 4.92 59.4%
## age = adult         4  0.2623 [-0.5481;  1.0727] 0.1461 0.3823 6.59 54.5%
## age = adolescence   1 -0.8127 [-1.5118; -0.1136]     --     -- 0.00    --
## 
## Test for subgroup differences (random effects model):
##                     Q d.f. p-value
## Between groups   6.13    2  0.0466
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = paste0(gender,':',env))

Subgroup analysis by “ed.level”

m.sg4sub <- update.meta(m.cont, subgroup = ed.level, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Flow state for women in stMale
## 
##                               SMD             95%-CI %W(random)         ed.level
## S1                         0.5991 [-0.0366;  1.2348]       12.9  upper-secundary
## S2                        -0.1546 [-0.6948;  0.3856]       14.4  upper-secundary
## S3                        -0.3863 [-1.0761;  0.3035]       12.2  upper-secundary
## S4                         0.7135 [-0.0246;  1.4516]       11.5 higher-education
## S5                         0.1435 [-0.5478;  0.8348]       12.1 higher-education
## S6                         0.6749 [-0.0769;  1.4266]       11.3 higher-education
## S7                        -0.3427 [-0.9389;  0.2536]       13.5          unknown
## S10: Only use prompt msgs -0.8127 [-1.5118; -0.1136]       12.0  upper-secundary
## 
## Number of studies combined: k = 8
## Number of observations: o = 298
## 
##                         SMD            95%-CI    t p-value
## Random effects model 0.0401 [-0.4281; 0.5083] 0.20  0.8453
## 
## Quantifying heterogeneity:
##  tau^2 = 0.1887 [0.0169; 1.2175]; tau = 0.4344 [0.1300; 1.1034]
##  I^2 = 61.6% [16.9%; 82.2%]; H = 1.61 [1.10; 2.37]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  18.22    7  0.0110
## 
## Results for subgroups (random effects model):
##                               k     SMD            95%-CI  tau^2    tau    Q   I^2
## ed.level = upper-secundary    4 -0.1755 [-1.1071; 0.7561] 0.2294 0.4790 9.24 67.5%
## ed.level = higher-education   3  0.4922 [-0.3173; 1.3017]      0      0 1.55  0.0%
## ed.level = unknown            1 -0.3427 [-0.9389; 0.2536]     --     -- 0.00    --
## 
## Test for subgroup differences (random effects model):
##                     Q d.f. p-value
## Between groups   7.16    2  0.0279
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = paste0(gender,':',env))

Subgroup analysis by “intervention”

m.sg4sub <- update.meta(m.cont, subgroup = intervention, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Flow state for women in stMale
## 
##                               SMD             95%-CI %W(random)
## S1                         0.5991 [-0.0366;  1.2348]       12.9
## S2                        -0.1546 [-0.6948;  0.3856]       14.4
## S3                        -0.3863 [-1.0761;  0.3035]       12.2
## S4                         0.7135 [-0.0246;  1.4516]       11.5
## S5                         0.1435 [-0.5478;  0.8348]       12.1
## S6                         0.6749 [-0.0769;  1.4266]       11.3
## S7                        -0.3427 [-0.9389;  0.2536]       13.5
## S10: Only use prompt msgs -0.8127 [-1.5118; -0.1136]       12.0
##                                                                   intervention
## S1                        Gender-stereotype color, ranking, badges, and avatar
## S2                        Gender-stereotype color, ranking, badges, and avatar
## S3                        Gender-stereotype color, ranking, badges, and avatar
## S4                        Gender-stereotype color, ranking, badges, and avatar
## S5                        Gender-stereotype color, ranking, badges, and avatar
## S6                        Gender-stereotype color, ranking, badges, and avatar
## S7                        Gender-stereotype color, ranking, badges, and avatar
## S10: Only use prompt msgs      Gender-stereotyped motivational message prompts
## 
## Number of studies combined: k = 8
## Number of observations: o = 298
## 
##                         SMD            95%-CI    t p-value
## Random effects model 0.0401 [-0.4281; 0.5083] 0.20  0.8453
## 
## Quantifying heterogeneity:
##  tau^2 = 0.1887 [0.0169; 1.2175]; tau = 0.4344 [0.1300; 1.1034]
##  I^2 = 61.6% [16.9%; 82.2%]; H = 1.61 [1.10; 2.37]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  18.22    7  0.0110
## 
## Results for subgroups (random effects model):
##                                                      k     SMD             95%-CI  tau^2    tau     Q   I^2
## intervention = Gender-stereotype color, rankin ...   7  0.1498 [-0.2943;  0.5939] 0.1147 0.3387 12.14 50.6%
## intervention = Gender-stereotyped motivational ...   1 -0.8127 [-1.5118; -0.1136]     --     --  0.00    --
## 
## Test for subgroup differences (random effects model):
##                     Q d.f. p-value
## Between groups   5.78    1  0.0162
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = paste0(gender,':',env))

Subgroup analysis by “age:intervention”

m.sg4sub <- update.meta(m.cont, subgroup = `age:intervention`, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Flow state for women in stMale
## 
##                               SMD             95%-CI %W(random)
## S1                         0.5991 [-0.0366;  1.2348]       12.9
## S2                        -0.1546 [-0.6948;  0.3856]       14.4
## S3                        -0.3863 [-1.0761;  0.3035]       12.2
## S4                         0.7135 [-0.0246;  1.4516]       11.5
## S5                         0.1435 [-0.5478;  0.8348]       12.1
## S6                         0.6749 [-0.0769;  1.4266]       11.3
## S7                        -0.3427 [-0.9389;  0.2536]       13.5
## S10: Only use prompt msgs -0.8127 [-1.5118; -0.1136]       12.0
##                                                                          age:intervention
## S1                        adolescent:Gender-stereotype color, ranking, badges, and avatar
## S2                        adolescent:Gender-stereotype color, ranking, badges, and avatar
## S3                        adolescent:Gender-stereotype color, ranking, badges, and avatar
## S4                             adult:Gender-stereotype color, ranking, badges, and avatar
## S5                             adult:Gender-stereotype color, ranking, badges, and avatar
## S6                             adult:Gender-stereotype color, ranking, badges, and avatar
## S7                             adult:Gender-stereotype color, ranking, badges, and avatar
## S10: Only use prompt msgs     adolescence:Gender-stereotyped motivational message prompts
## 
## Number of studies combined: k = 8
## Number of observations: o = 298
## 
##                         SMD            95%-CI    t p-value
## Random effects model 0.0401 [-0.4281; 0.5083] 0.20  0.8453
## 
## Quantifying heterogeneity:
##  tau^2 = 0.1887 [0.0169; 1.2175]; tau = 0.4344 [0.1300; 1.1034]
##  I^2 = 61.6% [16.9%; 82.2%]; H = 1.61 [1.10; 2.37]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  18.22    7  0.0110
## 
## Results for subgroups (random effects model):
##                                                          k     SMD             95%-CI  tau^2    tau    Q
## age:intervention = adolescent:Gender-stereotype co ...   3  0.0211 [-1.2371;  1.2793] 0.1492 0.3863 4.92
## age:intervention = adult:Gender-stereotype color,  ...   4  0.2623 [-0.5481;  1.0727] 0.1461 0.3823 6.59
## age:intervention = adolescence:Gender-stereotyped  ...   1 -0.8127 [-1.5118; -0.1136]     --     -- 0.00
##                                                          I^2
## age:intervention = adolescent:Gender-stereotype co ... 59.4%
## age:intervention = adult:Gender-stereotype color,  ... 54.5%
## age:intervention = adolescence:Gender-stereotyped  ...    --
## 
## Test for subgroup differences (random effects model):
##                     Q d.f. p-value
## Between groups   6.13    2  0.0466
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = paste0(gender,':',env))

Subgroup analysis by “ed.level:intervention”

m.sg4sub <- update.meta(m.cont, subgroup = `ed.level:intervention`, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Flow state for women in stMale
## 
##                               SMD             95%-CI %W(random)
## S1                         0.5991 [-0.0366;  1.2348]       12.9
## S2                        -0.1546 [-0.6948;  0.3856]       14.4
## S3                        -0.3863 [-1.0761;  0.3035]       12.2
## S4                         0.7135 [-0.0246;  1.4516]       11.5
## S5                         0.1435 [-0.5478;  0.8348]       12.1
## S6                         0.6749 [-0.0769;  1.4266]       11.3
## S7                        -0.3427 [-0.9389;  0.2536]       13.5
## S10: Only use prompt msgs -0.8127 [-1.5118; -0.1136]       12.0
##                                                                           ed.level:intervention
## S1                         upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S2                         upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S3                         upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S4                        higher-education:Gender-stereotype color, ranking, badges, and avatar
## S5                        higher-education:Gender-stereotype color, ranking, badges, and avatar
## S6                        higher-education:Gender-stereotype color, ranking, badges, and avatar
## S7                                 unknown:Gender-stereotype color, ranking, badges, and avatar
## S10: Only use prompt msgs       upper-secundary:Gender-stereotyped motivational message prompts
## 
## Number of studies combined: k = 8
## Number of observations: o = 298
## 
##                         SMD            95%-CI    t p-value
## Random effects model 0.0401 [-0.4281; 0.5083] 0.20  0.8453
## 
## Quantifying heterogeneity:
##  tau^2 = 0.1887 [0.0169; 1.2175]; tau = 0.4344 [0.1300; 1.1034]
##  I^2 = 61.6% [16.9%; 82.2%]; H = 1.61 [1.10; 2.37]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  18.22    7  0.0110
## 
## Results for subgroups (random effects model):
##                                                               k     SMD             95%-CI  tau^2    tau
## ed.level:intervention = upper-secundary:Gender-stereoty ...   3  0.0211 [-1.2371;  1.2793] 0.1492 0.3863
## ed.level:intervention = higher-education:Gender-stereot ...   3  0.4922 [-0.3173;  1.3017]      0      0
## ed.level:intervention = unknown:Gender-stereotype color ...   1 -0.3427 [-0.9389;  0.2536]     --     --
## ed.level:intervention = upper-secundary:Gender-stereoty ...   1 -0.8127 [-1.5118; -0.1136]     --     --
##                                                                Q   I^2
## ed.level:intervention = upper-secundary:Gender-stereoty ... 4.92 59.4%
## ed.level:intervention = higher-education:Gender-stereot ... 1.55  0.0%
## ed.level:intervention = unknown:Gender-stereotype color ... 0.00    --
## ed.level:intervention = upper-secundary:Gender-stereoty ... 0.00    --
## 
## Test for subgroup differences (random effects model):
##                      Q d.f. p-value
## Between groups   13.03    3  0.0046
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = paste0(gender,':',env))

Subgroup analysis by “age:ed.level:intervention”

m.sg4sub <- update.meta(m.cont, subgroup = `age:ed.level:intervention`, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Flow state for women in stMale
## 
##                               SMD             95%-CI %W(random)
## S1                         0.5991 [-0.0366;  1.2348]       12.9
## S2                        -0.1546 [-0.6948;  0.3856]       14.4
## S3                        -0.3863 [-1.0761;  0.3035]       12.2
## S4                         0.7135 [-0.0246;  1.4516]       11.5
## S5                         0.1435 [-0.5478;  0.8348]       12.1
## S6                         0.6749 [-0.0769;  1.4266]       11.3
## S7                        -0.3427 [-0.9389;  0.2536]       13.5
## S10: Only use prompt msgs -0.8127 [-1.5118; -0.1136]       12.0
##                                                                                 age:ed.level:intervention
## S1                        adolescent:upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S2                        adolescent:upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S3                        adolescent:upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S4                            adult:higher-education:Gender-stereotype color, ranking, badges, and avatar
## S5                            adult:higher-education:Gender-stereotype color, ranking, badges, and avatar
## S6                            adult:higher-education:Gender-stereotype color, ranking, badges, and avatar
## S7                                     adult:unknown:Gender-stereotype color, ranking, badges, and avatar
## S10: Only use prompt msgs     adolescence:upper-secundary:Gender-stereotyped motivational message prompts
## 
## Number of studies combined: k = 8
## Number of observations: o = 298
## 
##                         SMD            95%-CI    t p-value
## Random effects model 0.0401 [-0.4281; 0.5083] 0.20  0.8453
## 
## Quantifying heterogeneity:
##  tau^2 = 0.1887 [0.0169; 1.2175]; tau = 0.4344 [0.1300; 1.1034]
##  I^2 = 61.6% [16.9%; 82.2%]; H = 1.61 [1.10; 2.37]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  18.22    7  0.0110
## 
## Results for subgroups (random effects model):
##                                                                   k     SMD             95%-CI  tau^2    tau
## age:ed.level:intervention = adolescent:upper-secundary:Gend ...   3  0.0211 [-1.2371;  1.2793] 0.1492 0.3863
## age:ed.level:intervention = adult:higher-education:Gender-s ...   3  0.4922 [-0.3173;  1.3017]      0      0
## age:ed.level:intervention = adult:unknown:Gender-stereotype ...   1 -0.3427 [-0.9389;  0.2536]     --     --
## age:ed.level:intervention = adolescence:upper-secundary:Gen ...   1 -0.8127 [-1.5118; -0.1136]     --     --
##                                                                    Q   I^2
## age:ed.level:intervention = adolescent:upper-secundary:Gend ... 4.92 59.4%
## age:ed.level:intervention = adult:higher-education:Gender-s ... 1.55  0.0%
## age:ed.level:intervention = adult:unknown:Gender-stereotype ... 0.00    --
## age:ed.level:intervention = adolescence:upper-secundary:Gen ... 0.00    --
## 
## Test for subgroup differences (random effects model):
##                      Q d.f. p-value
## Between groups   13.03    3  0.0046
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = paste0(gender,':',env))

Funnel Plot

m.cont <- update.meta(m.cont, studlab = data$study)
summary(eggers.test(x = m.cont))
## Eggers' test of the intercept 
## ============================= 
## 
##  intercept        95% CI     t    p
##      4.642 -5.85 - 15.13 0.868 0.42
## 
## Eggers' test does not indicate the presence of funnel plot asymmetry.
funnel(m.cont, xlab = "Hedges' g", studlab = T, legend=T, addtau2 = T)